Heuijin Lim Moriond QCD, 8-15 March 2008 1

4343rdrd Rencontres de Moriond : QCD and High Energy Interactions Rencontres de Moriond : QCD and High Energy Interactions8-15 March 2008, La Thuile, Italy8-15 March 2008, La Thuile, Italy

Heuijin Lim (ANL)Heuijin Lim (ANL) on behalf of H1 and ZEUS collaborations

Diffraction at HERADiffraction at HERA

Measurements of inclusive diffractionMeasurements of inclusive diffraction Diffractive Parton DensitiesDiffractive Parton Densities Test of factorization in diffractive Final Test of factorization in diffractive Final StatesStates

Heuijin Lim Moriond QCD, 8-15 March 2008 2

Inclusive Diffraction in Deep Inelastic Inclusive Diffraction in Deep Inelastic ScatteringScattering

22 )( kkQ

Kinematics of ep eXp

Inclusive DISInclusive DIS processprocess

p)(2qQx 2

syq)(pW 2 22 )( ppkkMX

22

22

WQMQx X

IP

IP

22X

2

xx

QMQβ

2)( ppt IPpZL xEpx 1

In pQCD, Pomeron exchange can be described by two-gluon

exchange.

DIS : Probe structure of proton Diffractive DIS : Probe structure of colorless system, Pomeron, exchange

Diffractive DIS processDiffractive DIS process

N (MN)

Heuijin Lim Moriond QCD, 8-15 March 2008 3

Event selectionEvent selection

Inclusive DISInclusive DIS processprocess

Diffractive DIS processDiffractive DIS process

Large Large Rapidity Rapidity

GapGap

Outgoing protonLeading Proton SpectrometerLeading Proton Spectrometer

xL=1-xIP=p⁄Z/pZ

η=-ln(tan(θ/2)) ηmax

Mass of XMass of X MMXX

Scattered Scattered electronselectrons

LPS methodLPS method MMXX method method

LRG methodLRG method

Heuijin Lim Moriond QCD, 8-15 March 2008 4

Measurements of inclusive diffractive DISMeasurements of inclusive diffractive DISDiffractive cross-section : dσ (MX,W,Q2)/dMX

Comparison of diffractive and total γ*p scattering Q2 dependence of αIP(0) and rdiff(=σdiff/σtot)

Diffractive structure function : xIPF2D(3)(β ,xIP,Q2), xIPF2

D(4)(β ,xIP,Q2, t)

Q2 dependence and β dependence Comparison with MX, LRG and LPS measurements

Diffractive Parton Densities Diffractive Parton Densities Extract DPDFs from QCD fit to inclusive diffractive DISCombined QCD fit to inclusive diffractive and Dijets

Test of factorization in diffractive Final Test of factorization in diffractive Final StatesStates

Dijets in DIS and Photoproduction

Heuijin Lim Moriond QCD, 8-15 March 2008 5

Diffractive Cross Section with MDiffractive Cross Section with MXX methodmethod

• Within systematic errors, good agreement between FPCI and FPCII.

FPCI (98-99) : 4.2 pb-1 2.2 < Q2 < 80 GeV2

Nucl. Phys. B713, 3(2005) FPCII (99-00) : 52.4 pb-1

20 < Q2 < 450 GeV2 Submitted to Nucl. Phys. B. (arXiv:0802.3017)

Heuijin Lim Moriond QCD, 8-15 March 2008 6

Comparison of diffractive and total Comparison of diffractive and total γγ *p scattering*p scattering1 (0)tot

IPα2222

2tot

pγ )(W~)Q(x,Fx)(1Qα4πσ

1) (0)diffIPα 2(2

X

diffpγ

2)(W~dM

σd

• For Q2 < 20 GeV 2, α IPdiff(0) is consistent w

ith soft Pomeron. • For Q2 > 30 GeV2, data suggest increase with Q2. Regge factorisation breaking. • α IP

diff(0) is lower than α IPtot(0) :

Different Pomeron trajectory!

r = r = σσdiffdiff(0.28 < M(0.28 < MXX < 35 < 35 GeV)/GeV)/σσtottot

• Within the errors of the measurements, r is independent on W.• At W=220 GeV, r ~ 15.8 % at Q2= 4 GeV2

r ~ 5.0 % at Q2= 190 GeV2

r shows a logarithmic dependence on Q2.

Heuijin Lim Moriond QCD, 8-15 March 2008 7

QQ22 dependence of x dependence of xIPIPFF22D(3)D(3)

• For β≥ 0.9 (dominated by events with MX<2 GeV), Constant or slowly decreasing with Q2

Expect higher twist effect from

• For x=β xIP < 0.001, xIPF2

D(3) increases with increasing Q2. Positive scaling violations.

Suggest perturbative effects such as gluon emission

• For fixed β, Q2 dependence of xIPF2

D(3) changes with xIP. Inconsistent with the Regge factorisation hypothesis

Lq(q )

x = β xIP < 0.001

X

diffpγ

X

2X

22

2D(3)2IP dM

dσ2M

)M(QQα4π

1 Fx

Probability to find a quark carrying x=βxIP in a proton undergoing a diffractive process.

Heuijin Lim Moriond QCD, 8-15 March 2008 8

Diffractive structure function with LPS Diffractive structure function with LPS methodmethod

),((),(, IP2

2IR2IPIRIR

2IPIPIP

2D(4)2 QFt),xfn QFt)(xf t),x,Q,(F

The parameterization of xIP dependence gives the intercept of αIP.

20.040.08IP

21.40.7IP

0.010.02-IP

(syst.)GeV)0.07(stat.0.03(0)αGeV (syst.)0.7(stat.)7.2B

)0.02(model(syst.))0.02(stat.1.1(0)α

20.190.06IP

22.00.7IP

0.0400.020-IP

GeV0.06(0)αGeV5.5B

(model).)0.012(syst.)0.018(stat1.114(0)α

2SoftIP GeV(0) ~ 0.25α Soft!Not

Heuijin Lim Moriond QCD, 8-15 March 2008 9

Comparison of LRG with LPS Comparison of LRG with LPS measurementsmeasurements

• Ratio between LRG and LPS is independent of Q2, β and xIP within errors.

It shows 23~25 % of proton dissociation contribution in LRG data. For xIP > 0.01, their constant ratio tells that the LRG data also contain the reggeon contribution.

ZEUS LRG 00 (prel.), ZEUS LPS 00 (prel.)

H1 LRG H1 LRG with Mwith MNN<1.6 GeV<1.6 GeV

ZEUS LRG with MZEUS LRG with MNN < 2.3 GeV < 2.3 GeV

(LPS/LRG)(LPS/LRG) (LPS/LRG)(LPS/LRG)

Heuijin Lim Moriond QCD, 8-15 March 2008 10

Factorization in Diffractive DISFactorization in Diffractive DIS

)Q(z,σt),x,Q(z,fXp)p(γσ 2iγIP

2Dpi

*D*

fi/pD(z,Q2,xIP,t) : Probability to find in a proton, with

a probe of resolution Q2, parton i with momentum fraction z, under the condition that the proton remains intact and emerges with small energy loss, xIP, and momentum transfer, t.

Obey DGLAP universal for diffractive ep DIS (inclusive, Dijet, Cham)

Universal partonic cross sectionDiffractive parton distribution function

Diffractive DIS, like inclusive DIS, is Diffractive DIS, like inclusive DIS, is factorizable :factorizable :

Assumption : Proton vertex factorizationAssumption : Proton vertex factorization Shape of diffractive PDFs independent of xIP and t. )Q(z,ft),(xf t),x,Q(z,f 2

piIPD

pIPIP2D

pi

Regge motivated IP flux

At large xIP, a separately factorizable sub-leading exchange (IR), with different xIP dependence and partonic composition.

Heuijin Lim Moriond QCD, 8-15 March 2008 11

H1 2006 DPDF FitsH1 2006 DPDF Fits

• Fit H1 LRG data with Q2≥8.5 GeV2, MX>2 GeV, β≤0.8)• Parameterize the parton density

χ2 ~ 158/183 d.o.f., Q0

2=1.75 GeV2

• Effective Pomeron trajectory (Fit A) :

~70 % gluons in diffractive exchange

• Due to lack of sensitivity for the gluon density at high z. Fit B : using zg(z,Q0

2)=Ag

χ2 ~ 164/184 d.o.f. , Q02=2.5

GeV2

qq CBq

20 z)(1zA)Q(z, z

gCg

20 z)(1A)Q(z,g z

(model))0.008(exp.1.118α 0.0290.010IP

Heuijin Lim Moriond QCD, 8-15 March 2008 12

Diffractive dijets in DISDiffractive dijets in DIS

RapidityRapidityGapGap

Fit 2006 - B

zIP= longitudinal momentum fraction of color singlet carried by parton entering hard sub-process zIP distribution is sensitive to gluon DPDF.

• H1 Dijet data are in better agreement with H1 Fit B. • ZEUS Dijet data consistent with H1 Fit B and MRW 2006 fit.• Combined Fit to inclusive and Dijet data better constraint to quark and gluon densities, close to H1 Fit B.

H1 2007 Jets DPDF

Fit 2006 – AFit 2006 -- B

H1 2007 Jets DPDF

Heuijin Lim Moriond QCD, 8-15 March 2008 13

Diffractive dijets in Photoproduction (QDiffractive dijets in Photoproduction (Q22 ~ 0 GeV ~ 0 GeV22))

xγ = 1 xγ < 1

xγ = fraction of photon momentum in hard scattering.

Interactions destroy gap for resolved PHP.

• Dijets are suppressed by a factor~0.5 for direct and resolved γ. (big difference: ET

jet1 (ETjet2) > 5 (4)

GeV)

• Dijets are weakly suppressed by a factor ~ 0.87 for direct and resolved γ. (ET

jet1 (ETjet2) > 7.5 (6.5) GeV) ET distribution may not be well reproduced by NLO. Still work in progress.

Heuijin Lim Moriond QCD, 8-15 March 2008 14

ConclusionConclusion Inclusive diffraction was measured Inclusive diffraction was measured with high statistics with high statistics for a wide kinematic rangefor a wide kinematic range from low to high Q from low to high Q22. .

Good agreement with the results measured by MX, LPS and LRG methods. Diffractive DIS and total γ*p process cannot be described by an unique pomeron and r=σdiff(0.28 < MX < 35 GeV)/σtot decreases ~ ln(1+Q2). Indication for Regge factorisation breaking was seen in

Q2 dependence of αIPdiff(0)

Q2 dependence of xIPF2D(3) for fixed β and fixed xIP

Evidence for pQCD evolution with Q2 as xIP0 or β 0.

Combined QCD fitCombined QCD fit to inclusive diffractive DIS and Dijets to inclusive diffractive DIS and Dijets It improved the gluon structure at high z. Gluon dominated: ~ 70 %. Diffractive charm and Dijets DIS data are consistent with NLO predictions based on DPDFs from inclusive data. Diffractive Dijets in photoproduction

ZEUS : agreement with NLO prediction and no large suppression(~0.87).H1 : suppression(~0.5) ET

jet dependence is investigated.